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dc.contributor.advisorGera, Ralucca
dc.contributor.advisorRasmussen, Craig
dc.contributor.authorFletcher, Douglas M.
dc.date.accessioned2012-03-14T17:38:08Z
dc.date.available2012-03-14T17:38:08Z
dc.date.issued2007-06
dc.identifier.urihttp://hdl.handle.net/10945/3366
dc.description.abstractGiven a graph G and its vertex set V(G), the chromatic number, Chi(G), represents the minimum number of colors required to color the vertices of G so that no two adjacent vertices have the same color. The domination number of G, gamma(G), the minimum number of vertices in a set S, where every vertex in the set ( ) V G S is adjacent to a vertex in S. The dominator chromatic number of the graph, Chi subd (G) represents the smallest number of colors required in a proper coloring of G with the additional property that every vertex dominates a color class. The ordered triple, (a, b, c), is realizable if a connected graph G exists with gamma(G) = a, Chi(G) = b, and Chi subd (G) = c. For every ordered triple, (a, b, c) of positive integers, if either (a) a=1 and b=c greater or equal 2 or (b) 2 less than or equal a, b less than c and c less than or equal to a + b, , previous work has shown that the triple is realizable. The bounds do not consider the case . In an effort to realize all the ordered triples, we explore graphs and graph classes with a = b = c = k greater than or equal to 2.en_US
dc.description.urihttp://archive.org/details/realizabletriple109453366
dc.format.extentxiv, 27 p. : ill.en_US
dc.publisherMonterey, California. Naval Postgraduate Schoolen_US
dc.rightsThis publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.en_US
dc.subject.lcshGraph theoryen_US
dc.titleRealizable triples in dominator coloringsen_US
dc.typeThesisen_US
dc.contributor.corporateNaval Postgraduate School (U.S.)
dc.contributor.departmentApplied Mathematics
dc.description.serviceUS Army (USA) authoren_US
dc.identifier.oclc166345886
etd.thesisdegree.nameM.S.en_US
etd.thesisdegree.levelMastersen_US
etd.thesisdegree.disciplineApplied Mathematicsen_US
etd.thesisdegree.grantorNaval Postgraduate Schoolen_US
etd.verifiednoen_US


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